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   A High School level Problem (Interesting)
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   Author  Topic: A High School level Problem (Interesting)  (Read 8267 times)
daemonturk
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A High School level Problem (Interesting)  
« on: Jul 27th, 2009, 3:47am »
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A straight track on a hillside makes an angle of 50 degrees with the line of greatest slope and an angle of 11 degree 28 minutes with the horizontal. Find the angle the hillside makes with the horizontal.
 
 
Cookies goes to the shortest and simplest solution. Cheesy
« Last Edit: Jul 27th, 2009, 3:47am by daemonturk » IP Logged
Grimbal
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Re: A High School level Problem (Interesting)  
« Reply #1 on: Jul 27th, 2009, 4:24am »
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Are the 50 measured horizontally (as on a map) or in 3D?
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daemonturk
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Re: A High School level Problem (Interesting)  
« Reply #2 on: Jul 27th, 2009, 8:51am »
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For that particular angle, 3D.
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Grimbal
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Re: A High School level Problem (Interesting)  
« Reply #3 on: Jul 27th, 2009, 9:13am »
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18?
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daemonturk
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Re: A High School level Problem (Interesting)  
« Reply #4 on: Jul 27th, 2009, 9:21am »
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Correct. But working?
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Grimbal
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Re: A High School level Problem (Interesting)  
« Reply #5 on: Jul 27th, 2009, 9:35am »
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Let's call alpha = 1128, beta = 50, and gamma the hill slope.
 
If we take a unit length l of track and call h is the altitude difference, then
  h = lsin(alfa)
 
On the other side, if d is the distance along the greatest slope that has the same difference, we have
  d = lcos(beta)
and
  h = dsin(gamma)
 
All this together gives
  sin(gamma) = h/d = sin(alfa)/cos(beta).
 
It would be clearer with a picture that shows where the right angles are.
« Last Edit: Jul 27th, 2009, 9:36am by Grimbal » IP Logged
daemonturk
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Re: A High School level Problem (Interesting)  
« Reply #6 on: Sep 1st, 2009, 4:21am »
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Ya.
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